The U.S. Supreme Court will not review a Maryland law requiring applicants to provide a “good and substantial reason” to carry a weapon in public — passing again on an opportunity to clarify the limitations of the Second Amendment.

The case of Raymond Woollard, a Baltimore County man who sued after renewal of his concealed-carry handgun permit was denied, was among the dozens the court announced Tuesday that it would not hear.

The justices provided no explanation why they declined to review Mr. Woollard’s case, as is typical.

The decision comes after the high court in April also declined to hear challenges to a strict New York law that makes it difficult for residents to get a license to carry a concealed handgun in public.

But the court’s exclusion of the two cases doesn’t mean it won’t eventually rule on gun-control issues, said John Hudak, a fellow at the Brookings Institution who studies gun policy.

Gun litigation saw an upswing after the 2008 District of Columbia v. Heller decision in the U.S. Supreme Court that overturned the city’s longtime ban on most handgun ownership. But while that case established an individual right to own guns and keep them in the home, the landmark decision “left open more questions than it answered,” said Mr. Hudak.

Alan Gura, a prominent gun-rights lawyer who works with the Bellevue, Wash.-based Second Amendment Foundation and represented Mr. Woollard, called the ruling “disappointing.”

“The issue remains open. There will be additional cases that raise these type of issues,” said Mr. Gura, who also argued the Heller case before the Supreme Court. “I do anticipate at some point the Supreme Court will wade into this territory. They just decided not to do so today.”

Mr. Woollard initially filed a lawsuit challenging Maryland’s gun laws in 2010 after Maryland State Police and the state’s Handgun Permit Review Board declined to renew his handgun permit because he did not provide documents to “verify a threat beyond his residence,” as required by state law. The Navy veteran initially received a permit to carry a gun outside his home after a 2003 break in at his residence, which led to an armed confrontation.

Last year, a U.S. District Court ruling struck down Maryland’s permit law as unconstitutional, but the 4th U.S. Circuit Court of Appeals overturned that decision earlier this year.

Without review by the Supreme Court, Maryland — one of fewer than 10 so-called may-issue states in which the government can deny a concealed-carry permit even if certain criteria are met — can continue requiring permit seekers to show that they face a specific danger outside the home or that they need a gun as a retired law enforcement officer or to perform workplace duties.

Mr. Gura said he is setting his sights on a similar case out of New Jersey that he believes could have the next shot at the court’s consideration.

A federal appeals court this summer upheld a gun law in that state that requires a “justifiable need” for a person to be granted a permit to carry a gun in public. Mr. Gura said he plans to file a petition for the Supreme Court to consider the case by the Nov. 25 deadline.

“In the Maryland case, the appeals court assumed there was a right to carry a gun outside the home and then upheld restrictions of that right,” Mr. Gura said.